Statistics

20-30

Step 1: Identify the frequency of each class interval: 0-10 has frequency 3, 10-20 has frequency 7, 20-30 has frequency 15, 30-40 has frequency 8. Step 2: Find the class with maximum frequency. Step 3: The class 20-30 has the highest frequency of 15. Step 4: Therefore, the modal class is 20-30. The modal class contains the mode value.

24.67

Step 1: Calculate deviations di = xi - a: d1=-5, d2=-3, d3=0, d4=3, d5=5. Step 2: Calculate fi×di: 2×(-5)=-10, 3×(-3)=-9, 5×0=0, 4×3=12, 1×5=5. Step 3: Find Σfi×di = -10-9+0+12+5 = -2. Step 4: Find Σfi = 2+3+5+4+1 = 15. Step 5: Apply formula: Mean = a + (Σfi×di/Σfi) = 25 + (-2/15) = 24.67.

9

Step 1: Arrange data in order (already arranged): 4, 6, 8, 10, 12, 14. Step 2: Count observations: n = 6 (even number). Step 3: For even n, median = average of (n/2)th and ((n/2)+1)th observations. Step 4: Positions are 3rd and 4th observations: 8 and 10. Step 5: Median = (8 + 10)/2 = 9.

18

Step 1: Understand that cumulative frequency is the sum of all frequencies up to that class. Step 2: For class 10-20: cf = 4. Step 3: For class 20-30: cf = 4 + 8 = 12. Step 4: For class 30-40: cf = 4 + 8 + 6 = 18. Step 5: The cumulative frequency for class 30-40 is 18.